Undergraduate? No. We've had calculators able to solve undergraduate problems for decades. AI doesn't change the need to understand how calculus works any more than calculators did. The foundations remain valuable.
Graduate? Yes.
Graduate? Yes.
For publications and theses, as long as the final results hold and can be replicated and validated, I don’t see why we shouldn’t allow the wholesale use of LLMs
This is really just a glorified undergraduate education, the real point of graduate school is to learn to do real-world relevant research. For the latter, I think LLM use will be accepted but there will be a heavy expectation on the author of making the result very easily digestable for human mathematicians and linking it thoroughly with the existing literature - something that LLMs are very much not successful at, but a student might be able to do quite well with a mixture of expert guidance and personal effort.